Physics book like spivak's calculus

[Bashir Saddad]

Hello,
I am studying electromagnetism and I can't skip a topic and go to the next unless I learn it. Can anyone please suggest a physics book and a calculus book on multivariables as rigorous as spivak's calculus?
thanks

 

[clope023]

Hello,
I am studying electromagnetism and I can't skip a topic and go to the next unless I learn it. Can anyone please suggest a physics book and a calculus book on multivariables as rigorous as spivak's calculus?
thanks

https://www.amazon.com/dp/0738200565/?tag=pfamazon01-20

 

[Jorriss]

https://www.amazon.com/dp/0738200565/?tag=pfamazon01-20

I'm not familiar with this text but it covers very advanced topics. I kind of doubt that is a good book for someone who also asked for a book on multivariable calc.

To the OP, I don't have experience with this book but you may want to read about https://www.amazon.com/dp/0070049084/?tag=pfamazon01-20 more.

 

[sunjin09]

https://www.amazon.com/dp/0738200565/?tag=pfamazon01-20

This book is very difficult to read. Schwinger is famous for treating physics "overly formal". I attempted it a few years ago and quickly gave up, realizing I needed more math ( I resorted to Morse&Feshbach which led to another disaster...)

 

[clope023]

This book is very difficult to read. Schwinger is famous for treating physics "overly formal". I attempted it a few years ago and quickly gave up, realizing I needed more math ( I resorted to Morse&Feshbach which led to another disaster...)

I see what you mean, I tend to like formal rigour so Schwinger's text seems right up my alley. I wouldn't have even looked at it unless I had my courses in complex variables, PDE's and Fourier analysis though and even skimming the book seems very daunting. For a junior senior undergrad without as much math probably wangsness is a better text.

https://www.amazon.com/dp/0471811866/?tag=pfamazon01-20

 

[micromass]

For multivariable, I can recommend Fleming's "Functions in several variables". Quite rigorous and complete book, but also elementary. It goes right up to proving Stokes theorem.

 

[Mike706]

Spivak's 'Calculus on Manifolds' is a multivariable calculus book similar in rigor to Spivak's 'Calculus', as is Munkre's 'Analysis on Manifolds'. You should be able to handle the first 3 chapters of Calc on Manifolds with little issue (no issue if you have some linear algebra under your belt). Chapters 4 and 5 are much more difficult IMO.

You can try going right into them, but if it turns out to be too much Bachman's 'A Geometric Approach to Differential Forms' is a more elementary (but less rigorous) guide to the subject matter of these chapters. You could read this to get a feel for the material, and then go back to Calculus on Manifolds. If I recall correctly, both books are around 130 pages. Bachman's book mostly has problems with calculations as opposed to proofs, which would also be useful.